Question

The difference between the squares of two consecutive numbers is 35 what are the numbers

Answer 1

Answer:

r, s={+/-18, +/- 17}

PREMISES

r^2–(r+1)^2=35

ASSUMPTIONS

Let r=one of the numbers

Let s=the other number (r+1)

CALCULATIONS

r^2–(r+1)^2=35 (Expand the second term on the left side of the equation)

r^2–(r+1)(r+1)=35

r^2–[r^2+(1r+1r)+1]=35

r^2–(r^2+2r+1)=35

(r^2-r^2)-2r-1=35 (Combine like terms by parentheses to simplify the math)

0–2r-1=35

-2r-1=35

-2r-(1–1)=35+1 (Add 1 to both sides of the statement)

-2r-0=35+1

-2r=36

-2r/-2=36/-2

r=

+/- 18

and,

if s=r+1, then

s=-18+1

s=

+/- 17

and,

r, s=

{+/- 18, +/- 17}

PROOF

If r, s={+/- 18, +/- 17}, then the equations

(r^2)–(r+1)^2=35 bring

(-18)^2-(-17)^2=35

324–289=35 and

35=35 establish the roots (zeros) r, s={+/- 18, +/- 17} of the equation r^2–(r+1)^2=35

Answer 2

Step-by-step explanation:

I hope this can help you.